I prefer the former choice. The point being you are trying to assign a char * to a char [] which is what strcpy is for. Given you are manipulating initialized C strings in this case anyway, you might as well deal with char * throughout the code.

You can use also std::string name[10] instead of 2d char's array. In this case only you can assign new values to the strings through operator '='.
Otherwise you should to use array of char* and use strcpy() function for assignment.